Day 7(Analytical Geometry-Parabola)

General Equation of Parabola (Opening to X)

Ax²+Dx+Ey+F= 0

General Equation of Parabola (Opening to Y)

Cy²+Dx+Ey+F=0

Standard Equation (Vertext at Origin- Opening to Left)

y²=-4ax

Standard Equation (Vertext at Origin- Opening to Right)

y²=4ax

Standard Equation (Vertext at Origin- Opening Upward)

x²=4ay

Standard Equation (Vertext at Origin- Opening Downward)

x²=-4ay

Standard Equation (Vertext at H,K- Opening to Left)

(y-k)²=-4a(x-h)

Standard Equation (Vertext at H,K- Opening to Right)

(y-k)²=4a(x-h)

Standard Equation (Vertext at H,K- Opening Upward)

(x-h)²=4a(y-k)

Standard Equation (Vertext at H,K- Opening Downward)

(x-h)²=-4a(y-k)

Parabola Eccentricity

1

Latus rectum

4a

Vertex to Focus

a

Vertex to Directrix

a

Ratio and Proportion Horizontal Axis

Y1²/Y2²=X1/X2

Ratio and Proportion of Vertical Axis

X1²/X2²=Y1/Y2

Alcorcon’s Formula for area bounded by latus rectum and parabola

A=8/3 a²

h of a parabola in horizontal axis

E²-4CD/4CD

k of a parabola in a horizontal axis

k= -E/2C

h of parabola vertical axis

h=-D/2A

k of a parabola in vertical axis

k=D²-4AF/4AE